The 18.03 method however is as follows:

$2\frac{d^2y}{dx^2}-2\frac{dy}{dx}+y=2e^{-x}$

$(2D^2-2D+1)y=2e^{-x}$,

( where $\alpha=-1$ and $p(D)=2D^2-2D+1$ )

$y_p = \frac{2}{p(\alpha)}e^{-x} = \frac{2}{5}e^{-x}$

I don't know if the linear differential operator ($D$) is discussed in any part of MST209, if not the conclusion is simple: MIT 18.03 does a better job at teaching differential equations than MST209 since Matuck said that he $D$ operator plays an important role in the rest of 18.03 ( lectures 14-33 ).

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